en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^4/(e^x))

Solution

\frac{d}{d x} (\frac{x ^{4}}{e ^{x}})

Solution

\frac{x ^{3} ( 4 - x )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{e ^{x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{4} ) e ^{x} - \frac{d}{d x} ( e ^{x} ) x ^{4}}{( e ^{x} ) ^{2}}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (e^{x}) = e^{x}

= \frac{4 x ^{3} e ^{x} - e ^{x} x ^{4}}{( e ^{x} ) ^{2}}

Simplify

\frac{4 x ^{3} e ^{x} - e ^{x} x ^{4}}{( e ^{x} ) ^{2}} : \frac{x ^{3} ( 4 - x )}{e ^{x}}

= \frac{x ^{3} ( 4 - x )}{e ^{x}}

Popular Examples

derivative of x4^x

\frac{d}{d x} (x 4^{x})

derivative of x^{13}derivative of

x^{13}

implicit (dy)/(dx),(7xy+3)^2=14y implicit derivative

\frac{d y}{d x}, (7 x y + 3)^{2} = 14 y

y^{^{'}} - y = x y^{2}

(\partial)/(\partial x)(1/(x^{-1)+4y^{-1}})

\frac{\partial}{\partial x} (\frac{1}{x ^{- 1} + 4 y ^{- 1}})

Frequently Asked Questions (FAQ)

What is the derivative of (x^4/(e^x)) ?
The derivative of (x^4/(e^x)) is (x^3(4-x))/(e^x)
What is the first derivative of (x^4/(e^x)) ?
The first derivative of (x^4/(e^x)) is (x^3(4-x))/(e^x)